Question

The volumes of two cones are in the ratio 1:10 and the radii of the cones are in the ratio of 1:2 what is the ratio of their heights?

Answer 1

They are in ratio 2:5.

Answer 2

The ratio of height is$\bold"{\frac{2}{5}}$ .  

Solution:

The ratio of volume of the two cones is 1: 10

The ratio of the radii of the two cones is 1: 2

Now as we, all know the volume of the cone is$\frac{1}{3} \pi r^{2} h$

ow dividing the volume of the cones we get,

Simplifying the volume in simpler form, we get $\frac{h_{1}}{h_{2}}$

$\frac{1}{10}=\frac{\frac{1}{3} \pi 1 r^{2} h_{1}}{\frac{1}{3} \pi 4 r^{2} h_{2}}$

$\frac{4}{10}=\frac{h_{1}}{h_{2}}$

Therefore, the ratio of their heights is $\frac{2}{5}=\frac{h_{1}}{h_{2}}.$

Hence after dividing the volume of cone 1 and cone 2 we get the ratio of their height which is $\frac{2}{5}$.